Negative numbers

Negative numbers are numbers that are less than zero.

When you first encounter negative numbers they can be perplexing. How can a bowl contain less than zero oranges? In fact, the counting numbers cannot be negative for this reason. It makes no sense.

But when we use scalar numbers, we are measuring something like temperature or height, negative values are useful. (See Uses of negative numbers.)

We take a fixed point and call that zero. Measurements one way are positive, and they are negative the other way. Zero is neither positive nor negative.

Try this Adjust the arrow to see how negative numbers lie to the left of zero on the number line. The applet will not allow you to set the arrow to zero or a positive number.

The  '–'  sign

Negative numbers are indicated by placing a dash ( – ) sign in front, such as –5, –12.77. A negative number such as –6 is spoken as 'negative six'.

It also means 'subtract'

An unfortunate thing in math is that the   ' – '   symbol is used for two different things. It signifies a negative number, as described above, but it also means 'subtract' or 'minus'. For example 5–3 means 'subtract 3 from 5' with a result of 2. Here, the minus-sign means subtraction.

So, when talking about a negative number such as –4, train yourself to say 'negative four'  to avoid the confusion. The same confusion happens with the plus ( + ) sign. See Positive numbers.

See also Doing arithmetic with positive and negative numbers.

Comparing numbers

With all numbers, whether they are negative, zero or positive:

  • A number is greater than another when it is to the right on the number line.
  • Conversely a number is less than another when it is to the left on the number line.

So for example

  • –4 is less than –1
  • zero is greater than –120
  • 90 is greater than –1

Larger /smaller - watch out!

Avoid the words 'larger', 'bigger' and 'smaller' when comparing numbers. They can fool you.

For example is -1000 larger than -4?   It may look like it, but is not. -1000 is less than -4 because it is to the left on the number line. But when you use the word 'larger' you may think otherwise. Avoid these two words in math. Use 'less than' and 'greater than' instead.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values